# How many odd numbers are there, using the digits 5, 6, 7, 8, 9, 0, that are greater than 1,200,000 with the conditions a. no repetition and b. repetition?

##### 1 Answer

Apr 6, 2017

See below:

#### Explanation:

We're looking for odd numbers, using the digits 5, 6, 7, 8, 9, 0, that are greater than 1,200,000 with the conditions a. no repetition and b. repetition.

**a. no repetition**

The largest number I can construct with the given numbers is 987,650, which is less than 1,200,000, and so no numbers can be constructed that meet the conditions.

**b. repetition allowed**

If I am allowed to use the digits any number of times, I can construct numbers such as:

9,999,999

99,999,999

999,999,999

and do so infinitely many times.

If I'm constrained to use the number of places represented by the given 6 digits, I'll once again be unable to construct any number over 1,200,000 since the largest one that I could construct is 999,999.